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A166830 Number of n X 3 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nonincreasing order. 4
2, 8, 18, 33, 54, 82, 118, 163, 218, 284, 362, 453, 558, 678, 814, 967, 1138, 1328, 1538, 1769, 2022, 2298, 2598, 2923, 3274, 3652, 4058, 4493, 4958, 5454, 5982, 6543, 7138, 7768, 8434, 9137, 9878, 10658, 11478, 12339, 13242 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..41.

FORMULA

Empirical: a(n) = (n^3+6*n^2+11*n-6)/6.

a(n) = A167772(n+3,n). - Philippe Deléham, Nov 11 2009

a(n) = A227819(n+6,n+2). - Alois P. Heinz, Sep 22 2013

Empirical: a(n) = floor(A000292(n+1)^3/(A000292(n+1) + 1)^ 2). - Ivan N. Ianakiev, Nov 05 2013

From G. C. Greubel, May 25 2016: (Start)

Empirical G.f.: (-1 + 6*x - 6*x^2 + 2*x^3)/(1 - x)^4 + 1.

Empirical E.g.f.: (1/6)*(-6 + 18*x + 9*x^2 + x^3)*exp(x) + 1. (End)

EXAMPLE

All solutions for n=3

...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1

...1.1.1...1.1.1...1.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2

...2.1.1...2.2.1...2.2.2...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2

------

...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.1

...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2...2.2.1...2.2.1...2.2.2

...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2...2.2.1...2.2.2...2.2.2

MATHEMATICA

lst={}; Do[AppendTo[lst, n*(n+1)*(n+2)/6-2], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)

CROSSREFS

Sequence in context: A081324 A190787 A018229 * A072779 A292764 A198014

Adjacent sequences:  A166827 A166828 A166829 * A166831 A166832 A166833

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 21 2009

STATUS

approved

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Last modified February 25 12:53 EST 2021. Contains 341607 sequences. (Running on oeis4.)